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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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1569-3953
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Volume 19, Issue 1

Issues

L 2 error estimates for a nonstandard finite element method on polyhedral meshes

C. Hofreither
Published Online: 2011-05-27 | DOI: https://doi.org/10.1515/jnum.2011.002

Abstract

Recently, Hofreither, Langer and Pechstein have analyzed a nonstandard finite element method based on element-local boundary integral operators. The method is able to treat general polyhedral meshes and employs locally PDE-harmonic trial functions. In the previous work, the primal formulation of the method has been analyzed as an inexact Galerkin scheme, obtaining H 1 error estimates. In this work, we pass to an equivalent mixed formulation. This allows us to derive error estimates in the L 2-norm, which were so far not available. Many technical tools from our previous analysis remain applicable in this setting.

Keywords:: non-standard FEM; polyhedral meshes; BEM-based FEM; mixed formulation

About the article

Received: 2010-12-13

Published Online: 2011-05-27

Published in Print: 2011-05-01


Citation Information: Journal of Numerical Mathematics, Volume 19, Issue 1, Pages 27–39, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnum.2011.002.

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[2]
Clemens Hofreither, Ulrich Langer, and Steffen Weißer
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Steffen Weißer
Computers & Mathematics with Applications, 2014, Volume 67, Number 7, Page 1390
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Journal of Computational and Applied Mathematics, 2014, Volume 263, Page 202
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Sergej Rjasanow and Steffen Weißer
SIAM Journal on Numerical Analysis, 2012, Volume 50, Number 5, Page 2357
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Clemens Pechstein
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